With the advancement of optical temporal cloaking, this technology has attracted increasing attention, and the related theoretical and experimental studies were intensively carried out. Unlike spatial cloaking, which controls the path of electromagnetic wave propagation by manipulating controllable electromagnetic parameters of the medium, optical temporal cloaking does not result in light deviating from its expected spatial trajectory. Instead, the optical signals is divided into leading and trailing parts, which creates a temporal cloak window that can conceal events. Typically, two light signals are either speed up or slowed down, preventing them from reaching inside the temporal cloak window and interacting with non-emitting materials, thus rendering internal events unobservable to observers. This approach, which conceals events for a limited duration rather than the object itself, has broad application prospects in many fields. In this work, we explore the implementation of optical temporal cloaking via a chiral atomic medium with a five-level structure. By enhancing the laser control field and employing a weak probe field, coherent coupling between electric dipoles and magnetic dipoles can be induced during the transition process. Alterations to the external laser field allow for the control of magnetoelectric coupling, leading to significant chirality. Within the chosen five-level chiral atomic system, the generalized expressions in terms of the parameters related to the atomic medium and the light field are derived. Subsequently, based on the group refractive index, the output light pulse were calculated. Numerical calculations were then carried out to analyze the influence of the external field and the length of atomic medium for the five-level atomic system on the width of the temporal cloak window and the intensity of the light pulses that form the window. The results show that the input pulse generates left and right circularly polarized beams through the five-level chiral atomic medium. The intensity variation of the output pulse depends on the parameter of the external field, and the output time has different extents of advance or delay. An effective temporal window is formed within a certain parameter range. In the effective temporal window, the amplitude of the control field influences the width of the temporal window, while the phase of the control field hardly affect the window width. Furthermore, within the amplitude range of one of the two coupling fields, the temporal cloak window is nearly unaffected by that amplitude. Conversely, an increase in the amplitude of the other coupling field results in a reduction of the temporal cloak window width, while a weaker amplitude of the coupled field causes both output pulses to exhibit characteristics of speeding up. In a certain range of control field phase and coupling field phase, an effective cloaking time window can be observed, in which the optical pulse shows the opposite law to the control field phase change in the process of one of the coupling field phase change, while in the change process of the phase of the other coupling field, it shows a law similar to that of the control field phase change. As the length of the medium increases, the temporal window is gradually widened, but the intensity of the light pulse weakens due to increased loss in the medium. Therefore, it is necessary to avoid long transmission distance to ensure the effectiveness of optical temporal cloaking. Consequently, the acceleration and delay of the output pulses can be controlled effectively by manipulating the strength, phase, and detuning of the control and the coupling fields, and a significant temporal cloak window can be obtained, and this provides a tunable optical temporal cloaking scheme.